A new approximation to dependence function in bivariate extreme value distributions

Dependence structures of joint extreme events can be modeled by extreme value copulas characterized by Pickings dependence function. In this thesis, two new approaches using Kernel Regression and Bayesian methods are proposed to estimate Pickands dependence function. In the first approach, new data points obtained with Bernstein copula approximation which have flexible form can serve to estimate the unknown Pickands dependence function. Kernel Regression method is then used to derive an intrinsic estimator. The performance of the estimator is given by a simulation study. Test results mainly show that the estimator has a better performance than the conventional estimators. In the second approach, Initially, cubic B-spline regression is used to model the dependence function. Then, the estimator of Pickands dependence function is obtained by the Bayesian approach. Through the estimation process, the prior and the posterior distributions of the parameter vectors are provided. The posterior sampling algorithm is presented in order to approximate the posterior distribution. We give a simulation study to measure and compare the performance of the proposed Bayesian estimator of the Pickands dependence function. A real data example is also illustrated.